Question: Simplify the following expression: $ n = \dfrac{x - 3}{9x - 1} + \dfrac{-4}{7} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{x - 3}{9x - 1} \times \dfrac{7}{7} = \dfrac{7x - 21}{63x - 7} $ Multiply the second expression by $\dfrac{9x - 1}{9x - 1}$ $ \dfrac{-4}{7} \times \dfrac{9x - 1}{9x - 1} = \dfrac{-36x + 4}{63x - 7} $ Therefore $ n = \dfrac{7x - 21}{63x - 7} + \dfrac{-36x + 4}{63x - 7} $ Now the expressions have the same denominator we can simply add the numerators: $n = \dfrac{7x - 21 - 36x + 4}{63x - 7} $ $n = \dfrac{-29x - 17}{63x - 7}$